Strong Uniform Attractors for Nonautonomous Suspension Bridge-Type Equations

Abstract EN

We discuss long-term dynamical behavior of the solutions for the nonautonomous suspension bridge-type equation in the strong Hilbert space D(A)×H2(Ω)∩H01(Ω), where the nonlinearity g(u,t) is translation compact and the time-dependent external forces h(x,t) only satisfy condition (C*) instead of translation compact.

The existence of strong solutions and strong uniform attractors is investigated using a new process scheme.

Since the solutions of the nonautonomous suspension bridge-type equation have no higher regularity and the process associated with the solutions is not continuous in the strong Hilbert space, the results are new and appear to be optimal.